1. Field of the Invention
The present invention relates to an apparatus for estimating the quantity of air introduced into a cylinder of an internal combustion engine.
2. Description of the Related Art
Conventionally, there has been known an air quantity estimation apparatus for an internal combustion engine equipped with a supercharger which estimates cylinder air quantity, which is the quantity of air introduced into a cylinder of the engine, by use of a physical model representing behavior of air within an intake passage (refer to, for example, Japanese Kohyo (PCT) Patent Publication No. 2001-516421).
One conventional apparatus of such a type estimates throttle valve downstream pressure P(t), which is the pressure of air as measured on the downstream side of a throttle valve and which changes with elapse of time t, on the basis of a differential equation (dP(t)/dt=f(mt(t))), wherein the time derivative term dP(t)/dt of the throttle valve downstream pressure P(t) is represented by a function f(mt(t)) whose variable is throttle-passing air flow rate mt(t), which is the quantity of air passing around the throttle valve per unit time and which changes with elapse of time t.
Incidentally, an apparatus of such a type generally estimates cylinder air quantity by use of a microcomputer which carries out numerical calculations composed of mainly four arithmetic operations. Therefore, estimation of throttle valve downstream pressure on the basis of the above-mentioned differential equation requires use of a mathematical formula which approximates the differential equation and whose solutions can be obtained by using four arithmetic operations. Such a mathematical formula is obtained by discretizing the differential equation. Difference method is known to be a useful method for such discretization.
According to the difference method, the time derivative term dP(t)/dt of the throttle valve downstream pressure P(t) is replaced with a value obtained by dividing by a predetermined time step Δt the difference (P(t2)−P(t1) between a throttle valve downstream pressure P(t1) at a certain time t1 and a throttle valve downstream pressure P(t2) at time t2, which is later than the time t1 by the predetermined time step Δt (that is, the amount of change in the throttle valve downstream pressure P(t) between times t1 and t2), the time step Δt being equal to t2−t1. Moreover, the value of the right-hand side function f(mt(t)) of the above-mentioned differential equation can be replaced with the value of a function f(mt(t1)) obtained by using the throttle-passing air flow rate mt(t1) at time t1. Through these approximations, the above-mentioned differential equation is converted to Equation (1) shown below, and Equation (2) is derived from Equation (1).{P(t2)−P(t1)}/Δt=f(mt(t1))  (1)P(t2)=P(t1)+Δt·f(mt(t1))  (2)
Meanwhile, when the opposite sides of the above-mentioned differential equation are integrated from time t1 to time t2, there is derived the following Equation (3), which provides a mathematically exact solution of the differential equation.P(t2)=P(t1)+∫f(mt(t))dt (integral interval: t1≦t≦t2)   (3)
The above-described Equations (2) and (3) implies that the throttle valve downstream pressure P(t2) obtained from Equation (2) coincides with the throttle valve downstream pressure P(t2) obtained from Equation (3) when the product Δt·f(mt(t1)) of Equation (2) is equal to the integration of the function f(mt(t)) from time t1 to t2. That is, when the product Δt·f(mt(t1)) of Equation (2) is equal to the integration of the function f(mt(t)) of Equation (3) from time t1 to t2, the value of the function f(mt(t1)) is equal to the average value of the function f(mt(t)) from time t1 to time t2.
Accordingly, if the actual value of the function f(mt(t)), which represents the time derivative value of the throttle valve downstream pressure, does not change greatly during the time step Δt, the conventional apparatus can estimate the throttle valve downstream pressure with high accuracy.
In view of the above, the throttle-passing air flow rate mt(t) will be considered. FIG. 1 shows a change in the throttle-passing air flow rate mt(t) with the throttle valve downstream pressure P(t). A dotted curved line L1 of FIG. 1 shows the change in the case where the throttle valve opening is small, and a solid curved line L2 of FIG. 1 shows the change in the case where the throttle valve opening is large. The point PU of FIG. 1 indicates the pressure of air on the upstream side of the throttle valve (throttle valve upstream pressure).
In the case where the throttle valve opening is small, when a state in which the operation conditions (load, etc.) do not change (steady state) continues, the throttle valve downstream pressure P(t) converges to a steady value PL which is lower than the throttle valve upstream pressure PU. In this steady state, when the operation conditions change, the throttle valve downstream pressure P(t) changes mainly within a region A on the curve L1 of FIG. 1. That is, a change in the throttle-passing air flow rate mt(t) with a change in the throttle valve downstream pressure P(t) is very small. Accordingly, the actual value of the function f(mt(t)), which represents the time derivative value of the throttle valve downstream pressure P(t), does not change greatly, and thus, the conventional apparatus can estimate the throttle valve downstream pressure with high accuracy.
Meanwhile, when a steady state continues with the throttle valve opening being large, the throttle valve downstream pressure P(t) converges to a steady value PH which is approximately equal to the throttle valve upstream pressure PU. In this steady state, when the operation conditions change, the throttle valve downstream pressure P(t) changes mainly within a region B on the curve L2 of FIG. 1. That is, a change in the throttle-passing air flow rate mt(t) with a change in the throttle valve downstream pressure P(t) is very large. Accordingly, the actual value of the function f(mt(t)), which represents the time derivative value of the throttle valve downstream pressure P(t), changes greatly, and thus, the conventional apparatus cannot estimate the throttle valve downstream pressure with high accuracy.
A conceivable method for coping with the above-described problem is performing the calculation of the above-mentioned Equation (2) with the time step Δt being decreased. However, this method causes a problem that the calculation load of the microcomputer increases as the time step Δt decreases.